 3.13 Proof of Theorem REF . By Theorem REF , we have that \(\xi \)  is a proper class in \(\mathcal {C}\)  with enough \(\xi \) -projectives and enough \(\xi \) -injectives. If follows from [1]} that \((\mathcal {C}, \mathbb {E}_\xi , \mathfrak {s}_\xi )\)  is an extriangulated category. Moreover,
